evolutionary algorithm

Accurate prediction of dam breach parameters in embankment dams is an essential step in the risk management plan. Overtopping and piping are the leading causes of embankment failure in the world. The failure of this type of dam is typically proposed by hydrological and hydraulic computational models of the dam (Wahl, 1998). The relationships for assessing the breach and flow characteristics are generally obtained by artificial intelligence and regression analysis from case studies of historical dam failure. These models relate the input parameters such as the dam height (Hw) and the flow volume through the breach (Vw) to the observed breach parameters resulting from the actual failures. Several relationships have been proposed to calculate Qp as a function of Hw and Vw (De Lorenzo & Macchione, 2014; Hagen, 1982; Kirkpatrick, 1977; Singh & Snorrason, 1984; Hakimzadeh et al., 2014). Downstream sediment transport studies show that breach geometry directly affects the output hydrograph. Investigations on historical records for Qp determination show that Hw and Vw could provide more accurate results than El and Ew. Moreover, the combination of these parameters significantly increases computational accuracy (Thornton et al., 2011; Wang et al., 2018). Several laboratory and field studies have been performed to investigate the hydraulic properties of the breach and the output hydrograph in overtopping failure cases (Dhiman & Patra, 2017; Sadeghi et al., 2020; Vaskinn et al., 2004). Determination of the average breach width (Bave) is an essential factor in determining progressive erosion (Von Thun & Gillette, 1990; Froehlich, 1995) as well as the height of breach (Hb). The range of variation in Bave as a function of the dam height (Hd) is an important issue in the breach lateral evolution process (Johnson & Illes, 1976; Singh & Snorrason, 1984).

The proper estimation of sediment yield of rivers is important for planning and managing water resources. Various methods have been developed to determine the relationship between discharge and sediment concentration. Sediment rating curve is one of the most common methods for estimating the suspended sediment yield in rivers, which is always associated with a large error. In order to improve estimation of sediment yield using sediment rating curve, the equation coefficients can be optimized using artificial intelligence methods. The purpose of this research is to use a genetic algorithm to optimize the Sediment rating equation coefficients for Gorganroud river (Ghazaghli station) and Fariman river (Bagh Abbasi station). With this aim in mind, discharge and suspended sediment concentration data have been acquired for the stations. Sediment rating curve equation was calculated for each station with training data. Then an optimal coefficient of equation was achieved using genetic algorithm model defined in MATLAB 2017 software. The study results showed that the genetic algorithm model for Ghazaghli and Bagh Abbasi stations had a better performance than the sediment rating curve with the Nash-Sutcliff coefficient of 0.5 and 0.72 and coefficient of determination of 0.5 and 0.89, respectively. Also, the genetic algorithm for Bagh Abbasi Station with the limited samples has better accuracy than the sediment rating curve method. The study results indicate a high performance of the genetic algorithm in optimizing the coefficients of Sediment rating curve equation, especially in low data stations.

Determining the amount of watershed sedimentation and its spatial distribution by using field measurements in practice faces a serious challenge. In recent decades, hydrological models have been widely used by hydrologists and water resource managers as a tool for analysing water resource management systems. The SWAT model is one of the semi-physical and semi-distributed hydrological models that have been widely used in recent years. Despite the wide use of the SWAT, simulation of the sediment has been associated with a large error in comparison to flow. These errors may come from using empirical methods such as the sediment rating curve for estimating sediment based on measured data. Therefore, in this research, the capabilities of the genetic algorithm (GA) were used to optimize the relationship between discharge and sediment and further optimal equation used for calibration and validation of the model.

The studied area is Fariman dam watershed with an area of 278.8 km2 which is located at latitude of 35 ˚ 33' to 35˚ 41' and longitude of 59 ˚ 34' to 59 ˚ 44' in Razavi Khorasan province. In this study, SWAT model was used to simulate runoff and sediment yield of Fariman dam watershed. In order to run the model, meteorological and hydrometric data including daily rainfall and maximum and minimum temperatures and sediment yield and discharge data, soil and land use maps of the watershed were achieved from relevant resources. The capabilities of the genetic algorithm were used to optimize the discharge -sediment relationship and were compared with sediment rating curve. For this purpose, optimization problem was defined for the genetic algorithm in MATLAB software as a search space of continuous values of the discharge –sediment coefficients. After that, sediment yield was extracted based on discharge data and calculated monthly sediment for SWAT calibration and validation. Sensitivity analysis, calibration and validation of the model were performed using the SUFI-2 algorithm using SWAT-CUP software. For this purpose using high sensitive parameters, the model was calibrated and validated for the period of 1991 to 2000.

Optimal coefficients extracted by GA indicate a better performance of the genetic algorithm in estimating the sediment yield. The comparative results of the sediment estimation models, revealed better performance of the genetic algorithm with RMSE = 70.9, NSE =0.46 and R2= 0.72 than the sediment rating curve. According to senetivity analysis of SWAT model, twelve parameters for stream flow and seven parameters for sediment yield were found to be sensitive. The most sensitive parameters for stream flow were SCS runoff curve number (CN2), effective hydraulic conductivity in tributary channel (CH_K1) and base flow alpha factor for bank storage (ALPHA_BNK) and the most sensitive parameters for sediment yield were peak rate adjustment factor for sediment routing, USLE equation soil erodibility factor (USLE_K), sediment concentration in lateral flow and groundwater flow (LAT_SED) and exponent parameter for calculating sediment reentrained in channel sediment routing (SPEXP). The SWAT calibration and validation results showed that the Nash-Sutcliffe efficiency index for monthly sediment and discharge for calibration period was 0.75 and 0.73, respectively and in the validation period was 0.85 and 0.76, respectively. Calibration and validation of the SWAT model was done with genetic algorithm model as an optimal method for deriving sediment data from measured daily discharge. The Nash-Sutcliffe efficiency coefficient for monthly discharge was 0.75 and 0.85 in the calibration and validation periods. Nash-Sutcliffe efficiency coefficients for monthly sediment yield were 0.86 and 0.81 for the same periods. SWAT evaluation results indicate that the model simulation is acceptable for predicting sediment yield and river flow. The performance of SWAT model in predicting of sediment in low flow is poor, which can be due to the effect of the parameters and model simplifications in the simulation of the sediment load.

In this research, simulation of runoff and sediment flow for Fariman dam watershed was performed using SWAT model. For this purpose, the capabilities of the genetic algorithm were used to optimize the relationship between discharge and sediment yields; then the results were used to calibrate and validate the SWAT model. The results indicate that genetics algorithm can be used for optimizing coefficient of sediment discharge equation and the result is better than sediment rating curve. Simulation of watershed hydrology using SWAT shows that the capability of the model in prediction of sediment yield and water flow is good. Using genetic algorithm to optimize the relationship between discharge and sediment has an important role in extracting daily sediment yield and simulation accuracy of the model. Also, the use of evolutionary algorithms can have a significant role in extracting the discharge -sediment relations, which usually is accompanied with a large error in experimental models such as a sediment rating curve.

Nowadays, along with an increase in water needs, there is no balance between water demand and water supply in most regions of the country. Therefore, planning an appropriate policy to strike a balance between a declining water supply and an increasing demand to prevent a crisis is of utmost importance. The use of optimization methods in this context can be useful. Evolutionary algorithm methods are known as appropriate methods in this regard, and their suitable performance have been reported. Biogeography-based optimization (BBO) is a new evolutionary algorithm which its high performance in some aspects has been proved. The main objective of this study was to assess the performance of BBO in water resources management for the first time. Firstly, BBO was used for finding optimal points of three benchmark function including Sphere, Rosenbrock, and Bukin6; secondly, it was applied for an optimal operation of the Karon4 Reservoir with the aim of hydropower generation. In order to evaluate the performance of BBO, in addition to this method, the genetic algorithm (GA) and the nonlinear programming (NLP) were employed. The results of benchmark function showed that BBO delivered a better performance than the GA in finding the optimal points of three functions. Moreover, BBO reached an optimal solution with a higher degree of accuracy. In operation of the Karon 4 Reservoir, the results also indicated the high efficiency of BBO in extracting optimal operational policies in such circumstances; the objective function value of BBO at the best performance was 1.223, and, that for GA was 1.535. Furthermore, the global optimal solution obtained from NLP for this problem was 1.213.

Many algorithms and methods have been applied, so far, in order to operate reservoirs, optimally. Recently, the Cuckoo Optimization Algorithm (COA) as a new Evolutionary Algorithm (EA) has been utilized for solving a number of bench mark functions and real problems, and high performance and efficiency has been reported for solving difficult optimization problems. The main objective of the current study was an assessment of the COA efficiency in water resource systems in order to extract optimal operation policy for a reservoir with hydropower application. An application of this algorithm in a thirty-year operation of the Karun4 Reservoir was evaluated. The results were compared with those results of Genetic Algorithm (GA) outcomes. The results showed that the COA has a greater ability to reach optimal solution in comparison with the GA. The mean values of the objective functions were 6.34 and 9.28 for the COA and GA algorithms, respectively. Furthermore, the obtained results by the COA showed less difference to the global optimum.